band-edge steepness obtained from esaki/backward diode

1488 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 61, NO. 5, MAY 2014

Band-Edge Steepness Obtained FromEsaki/Backward Diode Current–Voltage

CharacteristicsSapan Agarwal, Member, IEEE, and Eli Yablonovitch, Fellow, IEEE

Abstract— While science has good knowledge of semiconductorbandgaps, there is not much information regarding the steepnessof the band edges. We find that a plot of absolute conductance,I /V versus voltage V , in an Esaki diode or a backward diodewill reveal a best limit for the band tails, defined by the tunnelingjoint density of states of the two band edges. This joint density ofstates will give information about the prospective subthresholdswing voltage that could be expected in a tunneling field-effecttransistor. To date, published current–voltage characteristicsindicate that the joint band-tail density of states is not steepenough to achieve <60 mV/decade. Heavy doping inhomogeneity,among other inhomogeneities, results in a gradual density ofstates extending into the bandgap. The steepest measured tunneldiodes have a tunneling joint density of states >90 mV/decade.

Index Terms— Backward diode, band tails, density of states,Esaki diode, subthreshold swing, tunneling, tunneling field-effecttransistor (TFET), Urbach tail.

I. INTRODUCTION

WHILE science has good knowledge on the magnitudeof semiconductor bandgaps, there is not much infor-

mation regarding the sharpness of the band edges. There isgreat interest in finding a band-edge steepness in the jointconduction/valence band density of states, sharper than thethermal Boltzmann limited value, 60 meV/decade. This isimportant for designing a steep tunneling field-effect transistor(TFET) [1] as well as a better backward diode [2]. Measure-ments of the optical Urbach tail (the rate at which opticalabsorption falls off for photon energies below the bandgap),indicate a joint density of states of 23 meV/decade for Si [3]and 17 mV/decade for GaAs [4]. This seems somewhatpromising but the results need to be validated by electricaltransport measurements. Ideally, TFETs, Esaki diodes, andbackward diodes have current–voltage (I–V ) characteristicsthat are controlled by the band edges, abruptly turning ON

when the conduction band on the n-side aligns with the valenceband on the p-side of a tunneling junction [5], sometimescalled the band-edge energy filtering mechanism. In actuality,the band edge is not perfectly sharp and there are states

Manuscript received October 16, 2013; revised February 25, 2014; acceptedMarch 14, 2014. Date of current version April 18, 2014. This work wassupported by the Center for Energy Efficient Electronics Science NSF underAward 0939514. The review of this paper was arranged by Editor G. Niu.

The authors are with the University of California at Berkeley, Berkeley, CA94720 USA (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2014.2312731

that extend into the bandgap, affecting the I–V character-istics of TFETs, Esaki diodes, and backward diodes [6].We analyze these I–V measurements to infer the joint con-duction/valence band density of states. Electrically measuredjoint density of states have generally indicated a steepness>90 meV/decade, unlike the optical Urbach measurements thatare <60 meV/decade in good semiconductors. We attributethis smearing to the spatial inhomogeneity, such as thicknessfluctuations, poor interfaces, inhomogeneous electrostatics,and doping inhomogeneity that appears in real devices. Thatsame finite density of states will limit the subthreshold swingvoltage of a TFET. Fortunately, these effects can possibly beeliminated or ameliorated.

In intrinsic GaAs, the optical absorption falls off at asemilog rate of 17 meV/decade [4]. Doping the GaAs causesthe absorption to fall off more gradually. When doped top ∼ 1020/cm3, the absorption falls off at a semilog rate>60 meV/decade [7]. This means that if a TFET is heavilydoped, it will never be able to use the density of statesenergy filtering mechanism to achieve a subthreshold swingvoltage <60 mV/decade. To interpret electrical transport mea-surements, we show that the absolute conductance, I /V versusbias voltage V , is proportional to the tunneling joint densityof states in Section II. The tunneling joint density of statesis the product the joint conduction/valence band density ofstates and the tunneling transmission probability. This meansthat two terminal I–V measurements can be used to determinethe steepness of the band edge.

Consequently, we can learn how steep a TFET could bewithout ever building the full TFET. In Section III, we analyzea variety of data from the literature to see what experimentalband-edge steepness has been achieved. Finally, in Section IV,we show how this method can be applied to TFETs.

II. INFORMATION FROM ABSOLUTE CONDUCTANCE

As an example, we consider the I–V characteristics oftwo InAs mesa homojunction Esaki diodes that were grownby Molecular Beam Epitaxy (MBE) [8]. The semilog I–V curves are plotted in Fig. 1(a) and the absolute con-ductance (I /V ) in Fig. 1(b). The log{absolute conductance}varies smoothly at V = 0, offering the prospect for aphysical interpretation in terms of fundamental semicon-ductor properties. Contrariwise, in Fig. 1(a), the semilogplot, log{current} versus V , diverges at V = 0, prevent-ing direct interpretation. Likewise, a plot of log{differentialconductance} diverges on a semilog plot at the Esaki peak,

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AGARWAL AND YABLONOVITCH: BAND-EDGE STEEPNESS OBTAINED FROM ESAKI/BACKWARD DIODE I –V CHARACTERISTICS 1489

Fig. 1. (a) I–V curves for two InAs Esaki diodes are plotted [8]. The diodewas formed through MBE growth and mesa isolation. The p-side doping is1.8×1019/cm3. At V = 0, log{current} diverges and so the logarithmic slopeis meaningless. (b) Alternatively, log{absolute conductance} passes smoothlythrough the origin. Increasing the doping results in a significant worsening ofsemilog conductance swing voltage in mV/decade.

preventing direct physical interpretation. Thus, a log{current}or a log{differential conductance} plot does not give usthe information we want. By contrast, in Fig. 1(b), thelog{absolute conductance}, log{I /V }, smoothly decreasesfrom reverse bias, through the origin, and all the way tothe forward Esaki region. Consequently, we can interpret thenumber of millivolts required to get a decade change inconductance. We will now show that the smoothly varyingabsolute conductance measures the tunneling joint density ofstates.

We consider the following model for the tunneling current:I ∝

∫( fC − fV ) × � × DJ (E) × ∂ E . (1)

The difference between the Fermi occupation probabilitieson the p and n sides is ( fC − fV ). � is the tunneling probabilityacross the junction and DJ (E) is the joint density of statesbetween the valence band on the p-side and the conductionband on the n-side. We are interested in measuring thetunneling joint density of states � × DJ (E) in the integrandof (1). The different components of the current integral areshown in Fig. 2(c)–(f), for different bias points. The decreasingtunneling probability is shown in Fig. 2(c). The joint densityof states, DJ (E), is shown in Fig. 2(d)–(f). The joint densityof states is the product of the band tail in the conduction banddensity of states, DC (E), and the band tail in the valence banddensity of states, DV (E), as shown in Fig. 2(d)–(f). Goingfrom bias points I–III, the joint density of states exponentiallyincreases. To measure � × DJ (E), we need to divide out theeffect of the Fermi functions, fC − fV . Since the area under thecurve fC − fV is proportional to the applied voltage, dividingby the voltage approximately eliminates its effect.

We quantitatively see this by multiplying and dividing (1)by the integral of the Fermi levels

I ∝∫

( fC − fV ) × ∂ E ×∫

( fC − fV ) × � × DJ (E) × ∂ E∫( fC − fV ) × ∂ E

(2a)

= qV ×∫

( fC − fV ) × � × DJ (E) × ∂ E∫( fC − fV ) × ∂ E

. (2b)

Fig. 2. (a) The I–V curve and (b) conductance for an Esaki diode is plotted.(c) The tunneling probability at different biases is shown. The band diagram,Fermi occupation difference and joint density of states are plotted for biaspoints (d) I, (e) II and (f) III. (For simplicity, we show conduction, DC (E),and valence, DV (E), band edges with equally sloping band tails.) Even thoughthe band edges do not overlap, the band tails still overlap, resulting in a finitejoint density of states. The joint density of states exponentially increases whenshifting the bias from point I to III and is proportional to absolute I /V . Toshow this, we need to divide out the effect of the Fermi functions, fC − fVfrom the current. Since the area under the curve fC − fV is proportional tothe voltage, dividing by the voltage eliminates its effect, approximately. I /Vin (b) decreases exponentially at forward bias as the joint density of statesdecreases its overlap and the tunneling probability decreases.

Fig. 3. Current integral (1)–(3) is graphically illustrated. (The Fermi functionsand joint density of states on the right, are rotated 90° from Fig. 2.) Theintegral is essentially given by an average of � × DJ (E) over an energyrange of 4kB T, as indicated by the shaded region.

The second term looks like a weighted average of� × DJ (E) over the Fermi functions

I ∝ qV × 〈� × DJ (E)〉 . (3)

This is shown in Fig. 3.In our method, we pay little attention to the shape of

the Fermi functions. As observed in Fig. 4(a), the ratio


Fig. 4. Normalized Fermi occupation probability, ( fC − fV )/V , is plottedat � = 300 K. This illustrates the energy range over which � × DJ (E) isaveraged. (a) For small biases <4kBT/q the shape barely changes and so thechange in I /V is only due to the change in � × DJ (E). (b) At larger biases,the Fermi function width starts to increase and is given by V. � × DJ (E) ischanging exponentially while ( fC − fV )/V is changing linearly. Therefore,I /V still primarily gives the change in � × DJ (E).

( fC − fV )/V barely changes for V < 4kBT. This means thatin this range, any change in I /V is due mainly to the changein � × DJ (E). Consequently, measuring I /V will give usexactly what we are interested in �× DJ (E). Fig. 4(b) shows( fC − fV )/V starts to broaden and the height decreases forV > 4kBT, but even at V = 400 mV there is at most a 4×correction, which can safely be neglected with respect to theexponential changes shown in Fig. 2.

The steepness of the tunneling joint density of states inmV/decade is given by

S�×D(E) ≡[d log 〈�×DJ (E)〉

dV

]−1

≈[d log (I/V )

dV

]−1

. (4)

This is called the semilog conductance swing voltage.Measuring the number of millivolts required to get a decadechange in conductance, gives the steepness of �× DJ (E) andthus the tunneling junction.

A. Interpreting the Tunneling Joint Density of States

The voltage dependence of � × DJ (E) can be dominatedby either the tunneling probability, �, or the joint densityof states, DJ (E). Toward forward bias, both the tunnelingprobability and the density of states will decrease to turn offthe tunneling.

Whether � or DJ (E), is the most dominant influence oncurrent will depend on the particular geometry and currentlevel. We distinguish the effects of the � and DJ (E) byapproximating: 〈�× DJ (E)〉 ≈ 〈�〉 × 〈DJ (E)〉 [9]. Evalu-ating (4), the semilog conductance swing voltage, S�×D(E),gives the sum of the logarithms[

d log (I/V )

dV

]−1

=[

d (log 〈�〉 + log 〈DJ (E)〉)dV

]−1

(5a)

[d log (I/V )

dV

]−1

= S�×D(E) =[

1

Stunnel+ 1

SDOS

]−1

(5b)

SDOS measures the steepness of the joint band edge densityof states in mV/decade: SDOS ≡ [d log〈DJ (E)〉/dV ]−1. Asobserved from Fig. 2(d)–(f), the energy averaged joint densityof states changes exponentially with bias. SDOS measuresthe joint density of states steepness, which is the band tailsteepness. Stunnel is the semilog slope measuring how steeplythe tunneling conductance prefactor changes with respect tobias: Stunnel = [

d log 〈�〉 /dV]−1. Using the Wentzel-Kramer-

Brillouin exponential [10] to evaluate Stunnel for a typicalp-n junction gives [11], [12]

Stunnel ≡(

d log(�)

dV

)−1

= 2V

|log(�)| . (6)

With both mechanisms present in any specific case, theobserved S�×D(E) will be steeper than with one mechanismalone, and consequently places a lower limit, SDOS > S�×D(E)

and Stunnel > S�×D(E). At high-current density, � is closeto 1, and |log(�)| is small, leading to an undesirably largeStunnel. Achieving a high steepness will then depend entirelyon SDOS.

Unfortunately, we observe that the experimental data isactually not very steep at all, calling into question the commonoptimistic predictions [1], [13], based on a perfectly steep bandedge. The key point is that SDOS, which is undoubtedly impor-tant at high-current density, is even worse than the measure-ments, SDOS > S�×D(E). Therefore, experimentally observedband-edge steepness is inadequate for the goal of a steepdevice at high current, irrespective of tunnel thickness modu-lation, which sometimes performs well at low-current density.

III. ANALYZING PUBLISHED DATA

In this section, we analyze the absolute conductance ofseveral different published tunnel diodes to determine theband-tail steepness. In Fig. 1, we show the current andconductance for an InAs homojunction diode at two differentdoping levels [8]. Since the conductance is proportional totunneling joint density of states, we can measure the inverseof the semilog slope of the conductance, S�×D(E), to find thesteepness of the tunneling joint density of states in mV/decade.This is indicated by the inverse slope of the diagonal linesin Fig. 1(b). When the n-side doping is increased from3 × 1018/cm3 to 1 × 1019/cm3, S�×D(E) drastically increasesfrom 180 mV/decade to 570 mV/decade. This clearly illus-trates the dangers of smearing a band edge by doping tooheavily.1

In Fig. 5, we show the current and absolute conductancefor a series of mesa GaAs homojunction diodes that weregrown by MBE [8]. The n-side doping is 3 × 1019/cm3

and the p-side doping varies from NA = 5 × 1018/cm3 to5 × 1019/cm3. As the doping, NA , is changed, the absoluteconductance changes by three orders of magnitude becausethe tunneling barrier thickness/depletion region thickness ischanging. Nonetheless, the semilog conductance swing voltageonly changes from 130 to 165 mV/decade. This small change

1Contact resistance might present problems at the highest conductance. If weassume the peak conductance is limited by the contacts, measuring at a pointwhere the conductance has decreased by a decade means that the contactswill have at worst a 10% effect.


Fig. 5. (a) J versus V and (b) G = J/V versus V for GaAs mesa diodes [8].The diodes were grown by MBE at ND = 3 × 1019/cm3. The semilogconductance swing voltage = 130 mV/decade and then gets worse at heavierdoping.

Fig. 6. (a) J versus V and (b) G = J/V versus V for a silicon Esakidiode formed by implantation to about n-p ∼ 1020/cm3 is plotted (samplePN-BF2–Q8 in [14]). The semilog conductance swing voltage =140 mV/decade regardless of the temperature. It appears to be limited byinhomogeneities and the presence of random dopant ions.

in swing accompanied by a large change in current indicatesthat the steepness cannot be a result of barrier thicknessmodulation. The barrier thickness modulation swing wouldhave a strong dependence of current/tunneling probability asindicated in (6). The conductance smoothly passes throughthe origin of voltage, revealing the tunneling joint density ofstates, as predicted in (3). In the negative differential resistanceregime, oscillations can occur during measurement that resultin unrealistically sharp features. Consequently, in Fig. 5(b), wemeasure an average swing through the entire Esaki regime.

In Fig. 6, we show the current and conductance for a siliconEsaki diode formed by implantation to ∼1 × 1020/cm3 (samplePN-BF2–Q8 in [14]). Here, we show the measurement at 295and 103 K. Similar to Fig. 5, the semilog conductance swingvoltage is 140 mV/decade.

In addition to analyzing Esaki diodes, we can also considerbackward diodes that are tunneling diodes optimized to turnON around zero bias. Backward diodes are usually specifiedby a figure of merit, the curvature coefficient γ , that canused to estimate the semilog conductance swing voltage.γ is given by

γ ≡ d2 I/dV 2

d I/dV

∣∣∣∣V =0

. (7)

To relate (7) to the semilog conductance swing voltage, weneed a simple model for the current. From Fig. 2, �× DJ (E)changes exponentially with bias and is therefore proportionalto exp(−V/V0), where V0 is the exponential slope andgives the tunneling steepness. The negative sign is associatedwith backward diode action. Replacing � × DJ (E) withexp(−V/V0) in the current, (1), gives

I ∝∫

( fC − fV ) × e−V/V0 × ∂ E . (8)

At small biases, we can Taylor expand the Fermi functionssuch that fC − fV ∝ V and so we get

I ∝ V × e−V/V0 . (9)

Plugging (9) into (7) gives

γ = −2/V0 (10)

V0 can be converted to mV/decade to give S�×D(E):S�×D(E) = ln(10) × V0. Combining this with (10) gives

S�×D(E) = ln(10) × V0 = ln(10) × 2/γ. (11)

To do better than 60 mV/decade the backward diode curva-ture coefficient should be γ > 80. This is twice the typical goalof γ > 40 for backward diodes. This can be seen from the factthat, we need to model the current as I ∝ V × exp(−V/V0)rather than I ∝ exp(−V/V0) − 1. The extra factor of V givesan extra factor 2 when taking the derivative.

The best backward diode curvature coefficient appears tobe γ = 47 [15] and γ = 50 [16]. One paper claimed aγ = 70 [17], but did not show the I–V curve. In all cases,they fall short of a semilog conductance swing voltage steeperthan 60 mV/decade.

In Fig. 7, a germanium backward diode with γ = 50is shown. Using (11) to calculate the semilog conductanceswing voltage gives 92 mV/decade, corresponding exactly tothe measured value in Fig. 7(b).

In Fig. 8, we show an InAs/AlSb/Al0.12Ga0.88Sb hetero-junction backward diode [15] with γ = 47 and a semilogconductance swing voltage of 98 mV/decade. In this diode, thetunneling barrier thickness is fixed by the AlSb thickness andso the conductance steepness is entirely due to the joint densityof states. While various nonidealities or leakage currents maybe limiting the device, this is the steepest turn ON that hasbeen measured in the InAs/AlSb/AlGaSb system.

IV. ANALYZING TFETS

We can apply the same analysis that we have done so farto TFETs. In a TFET, we can either make a two terminal


Fig. 7. (a) I versus V and (b) G = I/V versus V for a germanium backwarddiode [16]. The semilog conductance swing voltage = 92 mV/decade is thesteepest tunnel diode conductance swing voltage we could find in the literaturefor which an I–V curve was provided.

Fig. 8. (a) J versus V and (b) G = I/V versus V for anInAs/AlSb/Al0.12Ga0.88As heterojunction backward diode [15]. This diodehas one of the highest reported curvature coefficients, γ , and consequentlylowest semilog conductance swing voltage reported in the literature. It also hasone of the lowest doping levels of 1.4×1017/cm3 near the tunneling junction.

source–drain measurement, or a three terminal ID–VG

measurement. In either case, the current is given by (1). In athree terminal measurement the Fermi occupation probability,fC − fV , is fixed by source–drain voltage, VDS, while� × DJ (E) is changed by the applied gate bias. This meansthat measuring the subthreshold swing voltage will give thetunneling joint density of states. However, some voltage is

Fig. 9. (a) ID versus VD and (b) G = ID/VD versus VDfor an In53Ga0.47As TFET [18]. The measured subthreshold swingvoltage = 216 mV/decade while the semilog conductance swing voltage =165 mV/decade. Since the ID–VD characteristic is not limited by the gateoxide, it reveals the junction’s steeper intrinsic tunneling properties.

lost across the gate oxide and so the subthreshold swingvoltage is increased by a poor gate efficiency.

If we want to avoid any gate issues, we can also do a twoterminal measurement. If the critical tunneling junction is thesource–channel junction, we need to fix the VG–VD voltagewhile measuring ID–VS . Since the gate potential will have astrong influence on the channel potential, the drain will notbe able to effectively control the source–channel junction.On the other hand, if the critical tunneling junction is at thechannel–drain junction, we want to measure ID–VD whilefixing the VG–VS voltage.

In Fig. 9, we analyze the ID–VD characteristics of anIn0.53Ga0.47As TFET at fixed VG–VS voltage. The measuredsubthreshold swing voltage is 216 mV/decade owing tothe poor gate oxide [18]. The measured ID–VD semilogconductance swing voltage = 165 mV/decade. Since the ID–VD characteristic is not limited by the gate oxide deficiencies,it reveals the junction’s steeper intrinsic tunneling properties.

This shows the value of using the semilog conductanceswing voltage to analyze a TFETs potential performance whenthe gate oxide has poor quality.

In TFETs, subthreshold swing voltages <60 mV/decadehave been measured, but only at extremely low-currentdensities of ∼1 nA/μm [19]–[23]. We now explain whythis has not been observed in backward diodes and Esakidiodes. These diodes need heavy doping which moves theband overlap threshold to forward bias, where the low-currentdensities are obscured by leakage current. Consequently, thesemilog conductance swing voltage can only be measured athigher current densities where it is not as steep. Contrariwise,in a transistor, the gate potential can ensure a narrow tunnelingbarrier with less doping and under reverse bias. 2-terminalmeasurements on a 3-terminal device are needed, with thegate acting only to adjust Fermi Levels. Furthermore, thediode electrostatics is not optimized for barrier thicknessmodulation, while the sub-60 TFET results are likely to bedue to barrier thickness modulation [11], [12].


V. CONCLUSION

The absolute conductance, I /V , of either a tunneling diodeor of a TFET source–drain I–V , is proportional to the tunnel-ing joint density of states. This is true even as the applied volt-age passes through zero. The joint-density-of-states behavespoorly, which will limit the prospective subthreshold swingvoltage that we can expect from TFETs. This is likely dueto the many nonidealities that smear the band edges. As afirst step, doping which is inherently inhomogeneous, shouldbe eliminated. Ultimately, a sharp threshold may even requirestructural reproducibility at the single atom level.

ACKNOWLEDGMENT

The authors would like to thank P. Solomon [14] forproviding the raw data for them to analyze. The authors wouldalso like to thank S. Rommel for providing the raw data in [8]for them to analyze.

REFERENCES

[1] A. C. Seabaugh and Q. Zhang, “Low-voltage tunnel transistors forbeyond CMOS logic,” IEEE Proc., vol. 98, no. 12, pp. 2095–2110,Dec. 2010.

[2] J. N. Schulman and D. H. Chow, “Sb-heterostructure interband backwarddiodes,” IEEE Electron Device Lett., vol. 21, no. 7, pp. 353–355,Jul. 2000.

[3] T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limitingefficiency of silicon solar cells,” IEEE Trans. Electron Devices, vol. 31,no. 5, pp. 711–716, May 1984.

[4] S. R. Johnson and T. Tiedje, “Temperature dependence of the urbachedge in GaAs,” J. Appl. Phys., vol. 78, no. 9, pp. 5609–5613, 1995.

[5] J. Knoch, S. Mantl, and J. Appenzeller, “Impact of the dimensionalityon the performance of tunneling FETs: Bulk versus one-dimensionaldevices,” Solid-State Electron., vol. 51, pp. 572–578, Apr. 2007.

[6] M. A. Khayer and R. K. Lake, “Effects of band-tails on the subthresholdcharacteristics of nanowire band-to-band tunneling transistors,” J. Appl.Phys., vol. 110, no. 7, p. 074508, 2011.

[7] J. I. Pankove, “Absorption edge of impure gallium arsenide,” Phys. Rev.,vol. 140, pp. A2059–A2065, Mar. 1965.

[8] D. Pawlik et al., “Benchmarking and improving III-V esaki diodeperformance with a record 2.2 MA/cm2 peak current density to enhanceTFET drive current,” in Proc. IEEE IEDM, Dec. 2012, pp. 1–3.

[9] S. Agarwal, J. T. Teherani, J. L. Hoyt, D. A. Antoniadis, andE. Yablonovitch, “Engineering the electron-hole bilayer tunnelingfield-effect transistor,” IEEE Trans. Electron Devices, 2014, doi:10.1109/TED.2014.2312939.

[10] E. O. Kane, “Theory of tunneling,” J. Appl. Phys., vol. 32, no. 1,pp. 83–91, 1961.

[11] S. Agarwal and E. Yablonovitch, “Designing a low voltage, highcurrent tunneling transistor,” in CMOS and Beyond: Logic Switches forTerascale Integrated Circuits, T.-J. K. Liu and K. Kuhn, Eds. Cambridge,U.K.: Cambridge Univ. Press, 2014.

[12] S. Agarwal and E. Yablonovitch, “Fundamental tradeoff between con-ductance and subthreshold swing for barrier thickness modulation intunneling field effect transistors,” Under Review.

[13] M. Luisier and G. Klimeck, “Atomistic full-band design study of InAsband-to-band tunneling field-effect transistors,” IEEE Electron DeviceLett., vol. 30, no. 6, pp. 602–604, Jun. 2009.

[14] P. M. Solomon et al., “Universal tunneling behavior in technologi-cally relevant P/N junction diodes,” J. Appl. Phys., vol. 95, no. 10,pp. 5800–5812, 2004.

[15] Z. Zhang, R. Rajavel, P. Deelman, and P. Fay, “Sub-micron area hetero-junction backward diode millimeter-wave detectors with 0.18 pW/Hz 1/2

noise equivalent power,” IEEE Microw. Wireless Compon. Lett., vol. 21,no. 5, pp. 267–269, May 2011.

[16] J. Karlovsky and A. Marek, “On an Esaki diode having curvaturecoefficient greater than E/KT,” Czechoslovak J. Phys., vol. 11, no. 1,pp. 76–78, 1961.

[17] J. Karlovsky, “Curvature coefficient of germanium tunnel and backwarddiodes,” Solid-State Electron., vol. 10, no. 11, pp. 1109–1111, 1967.

[18] S. Mookerjea, D. Mohata, T. Mayer, V. Narayanan, and S. Datta,“Temperature-dependent I-V characteristics of a vertical In0.53Ga0.47Astunnel FET,” IEEE Electron Device Lett., vol. 31, no. 6, pp. 564–566,Jun. 2010.

[19] G. Dewey et al., “Fabrication, characterization, and physics of III-Vheterojunction tunneling field effect transistors (H-TFET) for steep sub-threshold swing,” in Proc. IEEE IEDM, Dec. 2011, pp. 1–4.

[20] T. Krishnamohan, K. Donghyun, S. Raghunathan, and K. Saraswat,“Double-gate strained-ge heterostructure tunneling FET (TFET) withrecord high drive currents and < 60 mV/dec subthreshold slope,” inProc. IEEE IEDM, San Francisco, CA, USA, Dec. 2008, pp. 1–3.

[21] S. H. Kim, H. Kam, C. Hu, and T.-J. K. Liu, “Germanium-source tunnelfield effect transistors with record high ION/IOFF,” in Proc. Symp. VLSITechnol., Kyoto, Japan, 2009, pp. 178–179.

[22] W. Y. Choi, B. G. Park, J. D. Lee, and T. J. K. Liu, “Tunnelingfield-effect transistors (TFETs) with subthreshold swing (SS) less than60 mV/dec,” IEEE Electron Device Lett., vol. 28, no. 8, pp. 743–745,Aug. 2007.

[23] K. Jeon et al., “Si tunnel transistors with a novel silicided source and46mV/dec swing,” in Proc. IEEE Symp. VLSI Technol., Honolulu, HI,USA, Jun. 2010, pp. 1–5.

Sapan Agarwal (M’06) received the B.S. degree inelectrical engineering from the University of Illinoisat Urbana-Champaign, Champaign, IL, USA, andthe Ph.D. degree from the University of California,Berkeley (UC Berkeley), CA, USA, in 2007 and2012, respectively.

He is currently a Post-Doctoral Fellow at UCBerkeley.

Eli Yablonovitch (F’92) received the Ph.D. degreein applied physics from Harvard University, Cam-bridge, MA, USA, in 1972.

He is a Professor of Electrical Engineering andComputer Sciences with the University of California,Berkeley, CA, USA, where he is the Director of theNSF Center for Energy Efficient Electronics Science.

band-edge steepness obtained from esaki/backward diode

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